Basic investigations on the freezing of human lymphocytes

Human lymphocytes were frozen at constant cooling rates in the range 2.4 to 1000 degrees K/min without cryoadditive on the cold stage of a thermally defined cryomicroscope. The volume loss due to water efflux was quantified optically for the cooling rates 2.4, 12, 48, and 120 degrees K/min. The likelihood of the formation of intracellular ice was determined as function of the cooling rate. Intracellular crystallization temperatures were obtained for ice formation during both cooling and rewarming. A theoretical analysis of the cell volume loss during freezing was compared to the experimental data and used for an indirect determination of the water permeability of the cells. A relative optimum of the cooling rate is predicted theoretically under the assumption of a critical level of intracellular salt concentration near the eutectic temperature. The dependence of survival and cooling rate was determined cryomicroscopically by simultaneously applying the FDA/EB fluorescence viability test. The optimal cooling rate of about 35 degrees K/min was also found for 2-ml samples frozen within the range of cooling rates of interest. The results show that for freezing in physiological saline solution (1) the optimum of the cooling rate is theoretically predictable, (2) cryomicroscopical data are significant for freezing of samples of larger volume, and (3) the lethal type of intracellular crystallization is cooling rate dependent and distinguishable from innocuous types.     

Nucleation and growth of ice crystals inside cultured hepatocytes during freezing in the presence of dimethyl sulfoxide.

A three-part, coupled model of cell dehydration, nucleation, and crystal growth was used to study intracellular ice formation (IIF) in cultured hepatocytes frozen in the presence of dimethyl sulfoxide (DMSO). Heterogeneous nucleation temperatures were predicted as a function of DMSO concentration and were in good agreement with experimental data. Simulated freezing protocols correctly predicted and explained experimentally observed effects of cooling rate, warming rate, and storage temperature on hepatocyte function. For cells cooled to -40 degrees C, no IIF occurred for cooling rates less than 10 degrees C/min. IIF did occur at faster cooling rates, and the predicted volume of intracellular ice increased with increasing cooling rate. Cells cooled at 5 degrees C/min to -80 degrees C were shown to undergo nucleation at -46.8 degrees C, with the consequence that storage temperatures above this value resulted in high viability independent of warming rate, whereas colder storage temperatures resulted in cell injury for slow warming rates. Cell damage correlated positively with predicted intracellular ice volume, and an upper limit for the critical ice content was estimated to be 3.7% of the isotonic water content. The power of the model was limited by difficulties in estimating the cytosol viscosity and membrane permeability as functions of DMSO concentration at low temperatures.     

Intracellular freezing of glycerolized red cells.

The response of glycerolized human red blood cells to freezing has been evaluated in terms of the thermodynamic state of the frozen intracellular medium. The physiochemical conditions requisite for intracellular freezing, characterized by the cooling rate and the degree of extracellular supercooling, are altered appreciably by the prefreezing addition of glycerol to the cells.Fresh human erythrocytes were suspended in an isotonic glycerol solution yielding a final cryophylactic concentration of either 1.5 or 3.0 m. Subsequently the cell suspension was frozen on a special low temperature stage, mounted on a light microscope, at controlled constant cooling rates with varying degrees of extracellular supercooling (ΔT_sc). The formation of a pure intracellular ice phase was detected by direct observation of the cells.The addition of glycerol produced several significant variations in the freezing characteristics of the blood. As in unmodified cells, the incidence of intracellular freezing increased with the magnitudes of both the cooling rate and the extracellular supercooling. However, the glycerolized cells exhibited a much greater tendency to supercool prior to the initial nucleation of ice. Values of ΔT_sc > ?20 °C were readily obtained. Also, the transition from 0 to 100% occurrence of intracellular ice covered a cooling rate spectrum in excess of 300 to 600 °K/min, as compared with 10 °C/min for unmodified cells. Thus, the incidence of intracellular ice formation was significantly increased in glycerolized cells.     

Stabilization of frozen Lactobacillus delbrueckii subsp. bulgaricus in glycerol suspensions: Freezing kinetics and storage temperature effects

The interactions between freezing kinetics and subsequent storage temperatures and their effects on the biological activity of lactic acid bacteria have not been examined in studies to date. This paper investigates the effects of three freezing protocols and two storage temperatures on the viability and acidification activity of Lactobacillus delbrueckii subsp. bulgaricus CFL1 in the presence of glycerol. Samples were examined at -196 degrees C and -20 degrees C by freeze fracture and freeze substitution electron microscopy. Differential scanning calorimetry was used to measure proportions of ice and glass transition temperatures for each freezing condition tested. Following storage at low temperatures (-196 degrees C and -80 degrees C), the viability and acidification activity of L. delbrueckii subsp. bulgaricus decreased after freezing and were strongly dependent on freezing kinetics. High cooling rates obtained by direct immersion in liquid nitrogen resulted in the minimum loss of acidification activity and viability. The amount of ice formed in the freeze-concentrated matrix was determined by the freezing protocol, but no intracellular ice was observed in cells suspended in glycerol at any cooling rate. For samples stored at -20 degrees C, the maximum loss of viability and acidification activity was observed with rapidly cooled cells. By scanning electron microscopy, these cells were not observed to contain intracellular ice, and they were observed to be plasmolyzed. It is suggested that the cell damage which occurs in rapidly cooled cells during storage at high subzero temperatures is caused by an osmotic imbalance during warming, not the formation of intracellular ice.     

An experimental comparison of intracellular ice formation and freeze-thaw survival of hela S-3 cells

A small-volume fluorescent dye viability assay has been successfully applied to a conduction cryomicroscope freezing-thawing stage as a means of determining post-thaw survival of the nucleated mammalian cell HeLa S-3. The survival signature for HeLa S-3 cells has been determined, revealing an optimum cooling rate of −30 °C/min where the maximum survival is 30%. No cells survive for cooling rates greater than −128 °C/min and the decreased survival at supraoptimal cooling rates coincides with a linear increase in the percentage of cells containing intracellular ice from 0% at −16 °C/min to 100% at −128 °C/min.Although no data were taken to identify increased salt concentration as the mechanism responsible for cell injury at suboptimal cooling rates, the post-thaw leakage of intracellular fluorescent dye at these rates takes approximately 4–10 min as opposed to instantaneous release of dye for cells which contain ice at the high cooling rates. This indicates two modes of damage.Cell number density has been identified as an important parameter in freezing studies since survival can be enhanced at slow rates by packing cells together in groups. Packing also causes a greater fraction of the cells in a sample to have intracellular ice present, thus decreasing survival at the faster rates. These responses can be explained by assuming that the outer cells in a group protect the inner ones from solution damage at slow rates, yet restrict water flux from the inner cells at faster rates, causing an increased likelihood of intracellular ice formation. Both of these results are consistent with the dual-mechanism freezing damage theory proposed by Mazur.     

Mechanism of cryoprotection by extracellular polymeric solutes.

To elucidate the means by which polymer solutions protect cells from freezing injury, we cooled human monocytes to -80 degrees C or below in the presence of various polymers. Differential scanning calorimetric studies showed that those polymers which protect cells best have a limiting glass transition temperature (T'g) of approximately -20 degrees C; those with a T'g significantly higher or lower did not protect. Freeze-etch electron micrographs indicated that intracellular ice crystals had formed during this freezing procedure, but remained smaller than approximately 300 nm in the same proportion of cells as survived rapid thawing. We propose that cryoprotection of slowly frozen monocytes by polymers is a consequence of a T'g of -20 degrees C in the extracellular solution. In our hypothesis, the initial concentration and viscosity of protective polymer solutions reduce the extent and rate of cell water loss to extracellular ice and limit the injurious osmotic stress, which cells face during freezing at moderate rates to -20 degrees C. Below -20 degrees C, glass formation prevents further osmotic stress by isolating cells from extracellular ice crystals, virtually eliminating cell water loss at lower temperatures. On the other hand, the protective polymer solutions will allow some diffusion of water away from cells at temperatures above T'g. If conditions are correct, cells will concentrate the cytoplasm sufficiently during the initial cooling to T'g to avoid lethal intracellular freezing between T'g and the intracellular Tg, which has been depressed to low temperatures by that concentration. Thus, when polymers are used as cryoprotective agents, cell survival is contingent upon maintenance of osmotic stress within narrow limits.     

A microscale model for prediction of breast cancer cell damage during cryosurgery

The morphology of cancerous breast tissue is characterized by tightly packed groups of small malignant cells, as found in most duct cell carcinoma. This special structure affects the osmotic responses of the cells to freezing and hence their probability of damage from cellular dehydration or intracellular ice formation. A mathematical model has been developed to study the microscale damage to these breast cancer cells during cryosurgery by accounting for their special structure. The model is based on a spherical unit comprised of an extracellular region that surrounds several layers of cancer cells, as experimentally observed of breast duct cell carcinoma by other researchers. Temperature transients in the breast cancer undergoing cryosurgery are calculated numerically using the Pennes equation. When subjected to various thermal histories, both cellular dehydration and intracellular ice formation in the unit structure are examined by considering the cell-to-cell contact and water transport at the microscale level. It is found that the cells in the inner layers hardly dehydrated while those in the outermost layer do greatly. The results help interpret the previously observed experimental phenomena that breast cancer tissues exhibit intracellular ice formation even at a slow cooling rate of -3 degrees C/min. In the attempt to better define an optimal procedure for breast cancer cryosurgery, various freezing protocols are simulated. The constant heat flux protocol induces greater cellular dehydration and higher intracellular ice formation probability simultaneously compared to the other protocols studied.     

A Cryomicroscopic Study of Cylindrocystis brebissonii De Bary and Two Species of Micrasterias Ralfs (Conjugatophyceae, Chiorophyta) during Freezing and Thawing

The changes in morphology of the unicellular algae Cylindrocystisbrebissonii and two species of Micrasterias during freezingand thawing were observed on a light microscope fitted witha temperature controlled stage. At slow rates of cooling extensiveshrinkage of the protoplast was observed. The response of thecell wall varied with cell-type. In C. brebissonii plasmolysiswas not observed and the cell wall and protoplast shrank together.In Micrasterias the cell wall did not contract and a distinctplasmolysis was observed. Following freezing to and thawingfrom –25?C cells of C. brebissonii were non-viable butremained osmotically responsive. Cooling at faster rates inducedintracellular ice formation in all cell-types. The criticalrate of cooling varied with cell-type and was determined bycell volume and suface area. Intracellular gas bubbles wereobserved during thawing following both rapid and slow cooling. Following cooling in dimethylsulphoxide cells of C. brebissoniiwere protected against freezing injury. The recovery on thawingfrom –196?C being determined by the rate of cooling, anoptimum rate of 1?C min^–1 was observed. During slow ratesof cooling (<2?C min^–1) cells remained unshrunken,at faster rates (10?C min^–1) the loss of cell viabilitywas related to osmotic shrinkage during cooling rather thanto nucleation of intracellular ice. Intracellular ice formationwas observed only following significantly faster rates of cooling(>20?C min^–1). Key words: Cylindrocystis, Micrasterias, cryomicroscopy, freezing injury     

A theoretical model of intracellular devitrification

Devitrification of the intracellular solution can cause significant damage during warming of cells cryopreserved by freezing or vitrification. Whereas previous theoretical investigations of devitrification have not considered the effect of cell dehydration on intracellular ice formation, a new model which couples membrane-limited water transport equations, classical nucleation theory, and diffusion-limited crystal growth theory is presented. The model was used to explore the role of cell dehydration in devitrification of human keratinocytes frozen in the presence of glycerol. Numerical simulations demonstrated that water transport during cooling affects subsequent intracellular ice formation during warming, correctly predicting observations that critical warming rate increases with increasing cooling rate. However, for cells with a membrane transport activation energy less than approximately 50 kJ/mol, devitrification was also affected by cell dehydration during warming, leading to a reversal of the relationship between cooling rate and critical warming rate. Thus, for low warming rates (less than 10 degrees C/min for keratinocytes), the size and total volume fraction of intracellular ice crystals forming during warming decreased with decreasing warming rate, and the critical warming rate decreased with increasing cooling rate. The effects of water transport on the kinetics of intracellular nucleation and crystal growth were elucidated by comparison of simulations of cell warming with simulations of devitrification in H(2)O-NaCl-glycerol droplets of constant size and composition. These studies showed that the rate of intracellular nucleation was less sensitive to cell dehydration than was the crystal growth rate. The theoretical methods presented may be of use for the design and optimization of freeze-thaw protocols.     

Subzero Osmotic Characteristics of Intact and Disaggregated Hepatocyte Spheroids

This study has been conducted to examine basic transport characteristics of pig hepatocytes cultured as spheroids for use in a bioartificial liver. Static osmotic experiments were conducted by subjecting hepatocyte spheroids in solutions of increasing sucrose concentrations. A Boyle-van't Hoff plot was used to extrapolate an osmotically inactive volume, V(b), of 0.60, which is unusually high and might not represent the inactive volume of the individual cells. The spheroids were disaggregated and low-temperature cryomicroscopy experiments performed to examine the transport and intracellular ice formation (IIF) characteristics. A hydraulic permeability, L(pg), of 7.6 x 10(15) m(3)/Ns and an activation energy, E(lp), of 82 kJ/mol was determined for the individual cells. The kinetic (Omega(o)) and thermodynamic (kappa(o)) coefficients for IIF were determined to be 5.9 x 10(8) m(-2) s(-1) and 3.0 x 10(9) K(5), respectively. These results infer a decrease in the temperature range over which IIF is observed compared to freshly isolated pig hepatocytes. The technique of freeze substitution was used to examine the structure inside the spheroid during freezing. At a low cooling rate of 1 degrees C/min, increasing amounts of intercellular ice formed between the cells. At a higher cooling rate of 100 degrees C/min small intracellular ice crystals formed. This study shows the location of ice in a freezing hepatocyte spheroid and confirms that the cells cultured as spheroids do not transport water in the same manner as isolated cells.     

A comparative study of the morphology and viability of hyphae of Penicillium expansum and Phytophthora nicotianae during freezing and thawing

The changes in morphology of Penicillium expansum Link and Phytophthora nicotianae Van Breda de Haan during freezing and thawing in a growth medium with and without the cryoprotective additive glycerol were examined with a light microscope fitted with a temperature-controlled stage. Viability of 0.5-1.0 mm diameter colonies of both fungi was determined after equivalent rates of cooling to -196 degrees C in the presence or absence of glycerol. In P. expansum shrinkage occurred in all hyphae at rates of cooling of less than 15 degrees C min-1; at faster rates intracellular ice nucleation occurred. The addition of glycerol increased the rate of cooling at which 50% of the hyphae formed intracellular ice from 18 degrees C min-1 to 55 degrees C min-1. This species was particularly resistant to freezing injury and recovery was greater than 60% at all rates of cooling examined. At rapid rates of cooling recovery occurred in hyphae in which intracellular ice had nucleated. In contrast, during the cooling of Ph. nicotianae in the growth medium, shrinkage occurred and no samples survived on thawing from -196 degrees C. However, on the addition of glycerol, shrinkage during freezing decreased and viable hyphae were recovered upon thawing; at rates of cooling over 10 degrees C min-1 the loss of viability was related to glycerol-induced osmotic shrinkage during cooling rather than to the nucleation of intracellular ice.     

Protective effect of intracellular ice during freezing?

Injury results during freezing when cells are exposed to increasing concentrations of solutes or by the formation of intracellular ice. Methods to protect cells from the damaging effects of freezing have focused on the addition of cryoprotective chemicals and the determination of optimal cooling rates. Based on other studies of innocuous intracellular ice formation, this study investigates the potential for this ice to protect cells from injury during subsequent slow cooling. V-79W Chinese hamster fibroblasts and Madin-Darby Canine Kidney (MDCK) cells were cultured as single attached cells or confluent monolayers. The incidence of intracellular ice formation (IIF) in the cultures at the start of cooling was pre-determined using one of two different extracellular ice nucleation temperatures (-5 or -10 degrees C). Samples were then cooled at 1 degrees C/min to the experimental temperature (-5 to -40 degrees C) where samples were warmed rapidly and cell survival assessed using membrane integrity and metabolic activity. For single attached cells, the lower ice nucleation temperature, corresponding to increased incidence of IIF, resulted in decreased post-thaw cell recovery. In contrast, confluent monolayers in which IIF has been shown to be innocuous, show higher survival after cooling to temperatures as low as -40 degrees C, supporting the concept that intracellular ice confers cryoprotection by preventing cell dehydration during subsequent slow cooling.     

Freezing injury to erythrocytes. I. Freezing patterns and post-thaw hemolysis.

The extent of hemolysis of human red blood cells suspended in different concentrations of glycerol and frozen at various cooling rates was investigated on the basis of morphological observation in the frozen state. Hemolysis of the cells in the absence of glycerol showed a V-shaped curve in terms of cooling rates. There was 70% hemolysis at an optimal cooling rate of approximately 10³ °C/min and 100% hemolysis at all other rates tested. Morphologically, a lower than optimal cooling rate resulted in cellular shrinkage, while a higher than optimal rate resulted in the formation of intracellular ice.The cryoprotective effect of glycerol was dependent upon its concentration and on the cooling rate. Samples frozen at 10³ and 10⁴ °C/min showed freezing patterns which differed from cell to cell. The size of intraand extracellular ice particles became smaller, and there was less shrinkage or deformation of cells as the rate of cooling and concentration of glycerol were increased.There was some correlation between the morphology of frozen cells and the extent of post-thaw hemolysis, but the minimum size of intracellular ice crystals which might cause hemolysis could not be estimated. As a cryotechnique for electron microscopy, the addition of 30% glycerol and ultrarapid freezing at 10⁵ °C/min are minimum requirements for the inhibition of ice formation and the prevention of the corresponding artifacts in erythrocytes.     

Osmotic response of individual cells during freezing. I. Experimental volume measurements

The osmotic response of yeast to freezing was measured as a function of cooling rate and degree of extracellular supercooling. Thirteen experimental trials were conducted on a cryomicroscope in which incremental size changes of individual cells were recorded photographically, and the corresponding volume variations were measured using a digital computer image analysis algorithm. Plots were obtained of normalized cell volume as a function of temperature. Cellular dehydration during freezing was progressively inhibited with increasing values of cooling rate and extracellular supercooling. Normalized cell volume changes were not a function of the relative initial cell size. A constant volume plateau occurred for conditions under which intracellular ice formation was expected.     

Water transport and IIF parameters for a connective tissue equivalent

Understanding the biophysical processes that govern freezing injury of a tissue equivalent (TE) is an important step in characterizing and improving the cryopreservation of these systems. TEs were formed by entrapping human dermal fibroblasts (HDFs) in collagen or in fibrin gels. Freezing studies were conducted using a Linkam cryostage fitted to an optical microscope allowing observation of the TEs cooled under controlled rates between 5 and 130 degrees C/min. Typically, freezing of cellular systems results in two biophysical processes that are both dependent on the cooling rate: dehydration and/or intracellular ice formation (IIF). Both these processes can potentially be destructive to cells. In this study, the biophysics of freezing cells in collagen and fibrin TEs have been quantified and compared to freezing cells in suspension. Experimental data were fitted in numerical models to extract parameters that governed water permeability, E(Lp) and L(pg), and intracellular ice nucleation, omega(o) and kappa(o). Results indicate that major differences exist between freezing HDFs in suspension and in a tissue equivalent. During freezing, 55% of the HDFs in suspension formed IIF as compared to 100% of HDFs forming IIF in collagen and fibrin TE at a cooling rate of 130 degrees C/min. Also, both the water permeability and the IIF parameters were determined to be higher for HDFs in TEs as compared to cell suspensions. Between the TEs, HDFs in fibrin TE exhibited higher values for the biophysical parameters as compared to HDFs in collagen TE. The observed biophysics seems to indicate that cell-cell and cell-matrix interactions play a major role in ice propagation in TEs.     

Stabilization of Frozen Lactobacillus delbrueckii subsp. bulgaricus in Glycerol Suspensions: Freezing Kinetics and Storage Temperature Effects

The interactions between freezing kinetics and subsequent storage temperatures and their effects on the biological activity of lactic acid bacteria have not been examined in studies to date. This paper investigates the effects of three freezing protocols and two storage temperatures on the viability and acidification activity of Lactobacillus delbrueckii subsp. bulgaricus CFL1 in the presence of glycerol. Samples were examined at −196°C and −20°C by freeze fracture and freeze substitution electron microscopy. Differential scanning calorimetry was used to measure proportions of ice and glass transition temperatures for each freezing condition tested. Following storage at low temperatures (−196°C and −80°C), the viability and acidification activity of L. delbrueckii subsp. bulgaricus decreased after freezing and were strongly dependent on freezing kinetics. High cooling rates obtained by direct immersion in liquid nitrogen resulted in the minimum loss of acidification activity and viability. The amount of ice formed in the freeze-concentrated matrix was determined by the freezing protocol, but no intracellular ice was observed in cells suspended in glycerol at any cooling rate. For samples stored at −20°C, the maximum loss of viability and acidification activity was observed with rapidly cooled cells. By scanning electron microscopy, these cells were not observed to contain intracellular ice, and they were observed to be plasmolyzed. It is suggested that the cell damage which occurs in rapidly cooled cells during storage at high subzero temperatures is caused by an osmotic imbalance during warming, not the formation of intracellular ice.     

Freezing response and optimal cooling rates for cryopreserving sperm cells of striped bass, Morone saxatilis

This study explored the optimization of techniques for sperm cryopreservation of an economically important fish species, the striped bass Morone saxatilis. The volumetric shrinkage or the water transport response during freezing of sperm cells was obtained using a differential scanning calorimeter (DSC) technique. Water transport was obtained in the presence of extracellular ice at a cooling rate of 20 degrees C/min in two different media: (1) without cryoprotective agents (CPAs), and (2) with 5% (v/v) dimethyl sulfoxide (DMSO). The sperm cell was modeled as a cylinder of length of 22.8 microm and diameter 0.288 microm and was assumed to have an osmotically inactive cell volume (V(b)) of 0.6 V(0), where V(0) is the isotonic or initial cell volume. By fitting a model of water transport to the experimentally determined water transport data, the best fit membrane permeability parameters (reference membrane permeability to water, L(pg) or L(pg)[cpa] and the activation energy, E(Lp) or E(Lp)[cpa]) were determined and ranged from L(pg)=0.011-0.001 microm/min-atm, and E(Lp)=40.2-9.2 kcal/mol). The parameters obtained in this study suggested that the optimal rate of cooling for striped bass sperm cells in the presence and absence of DMSO range from 14 to 20 degrees C/min. These theoretically predicted rates of optimally freezing M. saxatilis sperm compared quite closely with independent and experimentally determined optimal rates of cooling striped bass sperm.     

Cryobiology of rat embryos II: A theoretical model for the development of interrupted slow freezing procedures

Current mammalian embryo cryopreservation protocols typically employ an interrupted slow freezing (ISF) procedure. In general, ISF consists of initial slow cooling, which raises the extracellular solute concentration, and results in cell dehydration. Permeating cryoprotective agents (CPAs), such as dimethyl sulfoxide (DMSO), are typically included in the medium to protect the cells against high solute concentrations. As this ISF procedure continues, slow cooling is terminated at an intermediate temperature (T(p)), followed by plunging into liquid nitrogen (LN(2)). If the slow cooling step allowed a critical concentration ([CPA](c)) of CPA to be reached within the cell, the CPA will interact with the remaining intracellular water during rapid cooling, resulting in the majority of the intracellular solution becoming vitrified and preventing damaging intracellular ice formation (IIF). This study presents a theoretical model to develop efficient ISF procedures, on the basis of previously developed data for the rat zygote. The model was used to select values of initial CPA concentrations and slow cooling rates (from initial estimated ranges of 0 to 4 molal DMSO and 0 to 2.5 degrees C/min cooling rates) that would allow the intracellular solute concentration to exceed the critical concentration. The optimal combination was then determined from this range based on minimizing the duration of slow cooling.     

Is intracellular ice formation the cause of death of mouse sperm frozen at high cooling rates?

Mouse spermatozoa in 18% raffinose and 3.8% Oxyrase in 0.25 x PBS exhibit high motilities when frozen to -70 degrees C at 20-130 degrees C/min and then rapidly warmed. However, survival is <10% when they are frozen at 260 or 530 degrees C/min, presumably because, at those high rates, intracellular water cannot leave rapidly enough to prevent extensive supercooling and this supercooling leads to nucleation and freezing in situ (intracellular ice formation [IIF]). The probability of IIF as a function of cooling rate can be computed by coupled differential equations that describe the extent of the loss of cell water during freezing and from knowledge of the temperature at which the supercooled protoplasm of the cell can nucleate. Calculation of the kinetics of dehydration requires values for the hydraulic conductivity (Lp) of the cell and for its activation energy (Ea). Using literature values for these parameters in mouse sperm, we calculated curves of water volume versus temperature for four cooling rates between 250 and 2000 degrees C/min. The intracellular nucleation temperature was inferred to be -20 degrees C or above based on the greatly reduced motilities of sperm that underwent rapid cooling to a minimum temperature of between -20 and -70 degrees C. Combining that information regarding nucleation temperature with the computed dehydration curves leads to the conclusion that intracellular freezing should occur only in cells that are cooled at 2000 degrees C/min and not in cells that are cooled at 250-1000 degrees C/min. The calculated rate of 2000 degrees C/min for IIF is approximately eightfold higher than the experimentally inferred value of 260 degrees C/min. Possible reasons for the discrepancy are discussed.     

Equilibrium, quasi-equilibrium, and nonequilibrium freezing of mammalian embryos.

The first successful freezing of early embryos to -196 degrees C in 1972 required that they be cooled slowly at approximately 1 degree C/min to about -70 degrees C. Subsequent observations and physical/chemical analyses indicate that embryos cooled at that rate dehydrate sufficiently to maintain the chemical potential of their intracellular water close to that of the water in the partly frozen extracellular solution. Consequently, such slow freezing is referred to as equilibrium freezing. In 1972 and since, a number of investigators have studied the responses of embryos to departures from equilibrium freezing. When disequilibrium is achieved by the use of higher constant cooling rates to -70 degrees C, the results is usually intracellular ice formation and embryo death. That result is quantitatively in accord with the predictions of the physical/chemical analysis of the kinetics of water loss as a function of cooling rate. However, other procedures involving rapid nonequilibrium cooling do not result in high mortality. One common element in these other nonequilibrium procedures is that, before the temperature has dropped to a level that permits intracellular ice formation, the embryo water content is reduced to the point at which the subsequent rapid nonequilibrium cooling results in either the formation of small innocuous intracellular ice crystals or the conversion of the intracellular solution into a glass. In both cases, high survival requires that subsequent warming be rapid, to prevent recrystallization or devitrification. The physical/chemical analysis developed for initially nondehydrated cells appears generally applicable to these other nonequilibrium procedures as well.